The double-header hangover effect

The Pittsburgh Pirates’ pain continues to be this aspiring sabermetrician’s gain.

Three months ago, they won a 19-inning marathon against the St. Louis Cardinals. Reflecting on a 19-inning defeat they suffered to Atlanta the previous year that presaged their collapse back into the second division, I wrote a THT Live entry predicting that the win would have the opposite psychological effect, solidifying their playoff run. Instead, the Pirates collapsed again.

Hoping to retrieve something from my backfiring prediction, I looked into whether playing an extremely long baseball game (18 innings or more) had a harmful effect on a team in future games. To my rather pleased shock, I discovered that the effect does exist, lasting at least 30 days after the marathon game. The winner, on average, gets a boost for a week before sagging into a lengthy slump. The loser craters for the first week afterward, then has a rebound before settling into its own downward glide path. All told, after a marathon game a team can expect to under-perform by roughly one win over the next month.

Despite being my original hypothesis, this result surprised me, at least in the longevity of the effect. Some readers were dubious that the harm would last that long, and the small sample size I had to work with allowed for some skepticism along those lines (though the results were over two standard errors outside the norm, a generally accepted confidence level). Further evidence would help, if not from the exact situation then from a very similar one.

And there is a very similar case to playing an 18-inning (or more) baseball game: playing two baseball games in one day.

Double-headers are not a perfect match for a single marathon game. Teams have at least a day’s notice, and often much more, that they’ll be playing that much baseball that day. Managers can shape their lineups to give various players, almost always including catchers, part of the day off. They can handle bullpens in the first game with the foreknowledge that they need to leave something in reserve for the nightcap. The stress put on a team should be lessened.

On the other hand, it’s still 18 innings of baseball (or sometimes more, or very occasionally fewer). The combined fatigue accrued by the teams is going to be about the same, even if distribution may be changed. If two games’ worth of baseball is going to weaken a team for weeks, we should see it in this instance as well as in super-long games, though quite possibly lessened in intensity. And if the effect does not materialize, the results for marathon games come under greater doubt.

I followed a similar system in studying double-headers as I did for marathon games, checking a team’s win-loss performance for 30 days after playing a twin-bill, divided into sub-groups. I did not count subsequent games a team played against its double-header foe, since both teams fall equally under any fatigue effect, and the games they would play come out to a .500 record in any case. Games played after a significant rest (meaning the All-Star break) receive special consideration.

I got a larger sample size this time, thanks to double-headers being more common than 18-plus inning ballgames. I covered 74 double-headers played from 2009 to 2011. Retrosheet made 2012 game accounts available just too late for me to include.

My usual detour

Admittedly, 74 double-headers in three years is not a very great number. The species has become increasingly rare in our era, almost never occurring in nature. A day-nighter between Texas and Arizona on May 27, 2013 will apparently be the first scheduled major league double-header in several years. Any others come about through postponements, and with retractable roofs and modern groundskeeping, not to mention night baseball, those are much less common than they were.

I took a peek at the difference between today and bygone times in how many double-headers are played, and even my quick look at 1939 is astounding. In 2010, the whole of Major League Baseball played 17 double-headers. In 1939, no single team played fewer than 18. There were 205 double-headers that year, in a league with 1,232 scheduled games (and fewer actually completed) as opposed to 2,430 for the 2010 season.

Back in 2011, the Philadelphia Phillies felt burdened when they had to play three September double-headers in the span of 10 days, going 2-4 in those twin-bills. Back in 1939, the Brooklyn Dodgers played six double-headers in the last eight days of September—against four different teams, in four different cities (if you count Brooklyn as distinct from New York). They went 9-3 in those 12 games.

My baseball research retains its Socratic nature. The act of asking and answering one question reveals the next question needing to be asked. I’m going to be looking at old-time double-headers at some future date here at The Hardball Times—once I’ve finished answering the current question.

I found one other double-header curiosity. There were rare double-headers where one game ended before nine innings. In earlier times, it could have come via darkness, especially in late-season games when sunset arrived earlier. In the modern era, it comes almost exclusively because of rain.

Three of the double-headers I surveyed had nightcaps that ended before nine, all coming in 2009. Bizarrely, two of the three were Washington Nationals games that ended after 5 1/2 with the home-team Nats losing—and they came within a month of each other. Some things are just beyond human understanding, and that includes most of the stuff that happens in Washington.

(You may take that as a political crack, or as a Stephen Strasburg shutdown joke. It works either way.)

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Combined seasonal winning percentage for teams playing double-headers in this survey was .5056: This counts a team for each time it plays a double-header, and thus each time its future performance is measured. While “rematch” games against a double-header opponent are not counted, there are instances where teams play against another club that had a double-header in the previous 30 days. I let these games stay in the sample. Double-headers are frequent enough that having a couple of these instances is natural, and I’m not sure that the sample is any more “pure” for having them excised.

Tracking is broken down into the same groups as for my marathon game study: the first to third days after the double-headers, then days four to seven, eight to 10, 11 to 15, 16 to 20, and 21 to 30. I did it this way the first time to see when any damaging effect would wear off, only to find that it never fully did for those 30 days. This time around, things are different—but only a little different.

Some teams were playing double-headers late enough in the season that they weren’t playing games for 30 days thereafter. (The most extreme example were the 2010 Yankees and Red Sox playing two on the second to last day of the season.) I include their regular-season records as far as they go, and ignore any postseason play: the higher level of competition there would bias the results.

The first table is for all games, not counting “rematches.”

Group of days           1-3      4-7      8-10    11-15    16-20      21-30

D-H players' record   109-125  226-253  141-163  233-275  259-259    433-455
Winning percentage     .4658    .4718    .4638    .4587    .5000      .4876

Cumulative record     109-125  335-378  476-541  709-816  968-1075  1401-1530
Cumulative win pct.    .4658    .4698    .4680    .4649    .4738      .4780

This would be a good time to bring up my original article for some side-by-side comparison. The marathon sample showed significant variation between time groups, but the results always showed teams underperforming. With the larger sample size for double-headers, we see a smoother track to the numbers, especially in the first seven days, but the overall story is quite similar.

No time group shows the double-header players performing above .500, and this against a background record of .5056. The post-double-header record is pretty steady for the first 15 days, gets a bump in the next five, then settles back down slightly from day 21 to 30. The overall effect is not as strong as it was for marathons, but it is still there.

Again, a potential skewing factor is interruptions in play. The All-Star break gave a number of teams in this survey a nice breather, during which presumably they could recover from any fatigue remaining from a recent double-header. I removed any games coming after such breaks to get a modified set of numbers.

Group of days           1-3      4-7      8-10    11-15    16-20      21-30

D-H players' record   109-125  220-252  140-158  223-270  242-248    401-416
Winning percentage     .4658    .4661    .4698    .4523    .4939      .4908

Cumulative record     109-125  329-377  469-535  692-805  934-1053  1335-1469
Cumulative win pct.    .4658    .4660    .4671    .4623    .4701      .4761

Teams went 66-61 during the survey period in games after an All-Star break, so it seems they put their rest to good use. The overall winning percentages thus end up dropping in the modified survey, though the amount is about half what it was when I made the same modification in the marathon survey.

Despite the fall-off in performance being not as large, the confidence in this result is greater, due to the much larger sample size. The teams finished .0276 behind their season winning percentages, and .0295 for the modified numbers, both margins being greater than four standard errors. Confidence levels for both sets of figures work out to better than 99.5 percent (though I couldn’t get it to 99.9).

I can state my conclusion this time even more categorically than I did two months ago. Playing a double-header has a significant negative effect on the future play of a baseball team. For the first 15 days, it’s about as strong as that for a team playing an 18-inning (plus) game; over the following 15 days, it falls off to about half the intensity. Overall, the double-header “hangover” is about three-fourths as strong as the marathon “hangover” across one month, and costs a team around three-fourths of a win over that month.

To follow the parallel with my previous article to its conclusion, I will now examine whether winning, losing or splitting the double-header affects the strength of the hangover effect a team suffers afterward. “Rematch” games will be counted here, for the fullest possible comparison between winners, losers and splitters. Games after an All-Star break will once again be omitted.

Teams that swept their double-headers had an average season record of .5264; those who split played at .5123 over the full season; losers of their double-headers had season marks of .4723. That’s a wider separation than for the marathon games, maybe because the twin-bills are determining a greater proportion of those overall records. It’s against those figures that we measure their performance after the double-header.

Group of days         1-3      4-7      8-10     11-15     16-20     21-30

Winners' record      55-40    57-70    36-46     65-70     71-60    102-101
Winning percentage   .5789    .4488    .4390     .4815     .5420     .5025

Cumulative record    55-40   112-110  148-156   213-226   284-286   386-387
Cumulative win pct.  .5789    .5045    .4868     .4852     .4982     .4994

Splitters' record    88-88   107-128   84-78    116-128   122-123   218-237
Winning percentage   .5000    .4553    .5185     .4754     .4980     .4791

Cumulative record    88-88   195-216  279-294   395-422   517-543   735-780
Cumulative win pct.  .5000    .4745    .4869     .4835     .4877     .4851
Losers' record       35-66    63-61    34-48     50-80     56-72    107-105
Winning percentage   .3465    .5081    .4146     .3846     .4375     .5047

Cumulative record    35-66    98-127  132-175   182-255   238-327   345-432
Cumulative win pct.  .3465    .4356    .4300     .4165     .4212     .4440

The time subdivisions after the double-header show some serious volatility, especially for the teams sweeping and swept. Some of that in the first three days comes from sweepers having a 24-13 record in rematch games against the swept. That elevates the sweepers’ performance notably, though the swept were doing so badly that an added 13-24 actually lifted their winning percentage a bit. That big split, though, could well come from the double-header winners simply being better baseball teams, and continuing to play accordingly against lesser competition.

Beyond those first three days, the numbers are all over the place, with little or no pattern asserting itself. The figures for splitters are the least crazed, and one can maybe tease out a flat performance line a little under .500, affected by random fluctuations. (I note briefly that the two best records in the splitters’ subdivisions come from the smallest sample sizes, for days 1-3 and 8-10.) For the sweepers and swept, guessing at a pattern is a bad risk.

That volatility vanishes, though, when we look at the larger picture. Double-header winners performed .0270 below their season winning percentages over the full 30 days surveyed, while splitters lagged by .0272, and losers trailed their season numbers by .0283. That is a remarkably even set of numbers. One more win by the double-header losers, and the hangover effect would have been within .0002 for all three, about as close as the granularity of the data permitted. The specific result of the double-header has zero apparent effect on how a team plays afterward.

In the marathon survey, I found that losers had a significantly greater fall-off over a 30-day period than winners; for double-headers, the effect is nonexistent. The double-header figures have a much larger sample size backing them up, so I’m much more confident in them. Unless the psychological impact of losing one game in the 18th is much bigger than for losing two games in the ninth—which may be so—one can perhaps discount that result a little.

Beating the odds, and getting beaten

The best performances after a double-header suggest that Los Angeles and its environs are a great place to play two. The 2009 Angels went 19-8 for the 30 days after sweeping a twin-bill from Kansas City, though this isn’t such a huge leap up from their ultimate 97-65 record. If you want really improved performance, look to the 2010 Dodgers. They dropped a pair to the Mets on April 27, then went 18-9 over the next month. Given that they were a losing team over the whole season at 80-82, this shows some surprising resilience, with a .173 improvement over their season record after getting swept.

Teams were more likely to plummet than soar after a double-header, and the extremes are greater on the negative side. The 2009 Cleveland Indians, a 65-97 club, went a dismal 5-19 after losing a Texas twin-bill, while the 59-103 Washington Nationals of that same year staggered to a 5-21 mark in the 30 days after dropping two to the Phillies. Such awful records aren’t so surprising coming from cellar-dwellers: what would really impress would be a collapse or two by good teams, the kind of thing that could knock them out of pennant races.

Anyone who remembers the final month, and especially the final day, of the 2011 season may be able to guess what’s coming next.

The 2011 Atlanta Braves’ double-header at Citi Field on Sept. 8 seemed to be a respite, as they swept the Mets to rebound from a 1-5 slide. It was illusory: They had burned a day off to fit in those two rained-out games, and immediately had to wing off to St. Louis, where the Cardinals would sweep them to kick-start their own long-shot playoff run. Atlanta, 89-73 in 2011, went 5-13 for the rest of the season after their New York double-header, losing their Wild Card berth on the final day of the season to St. Louis.

The 2011 Boston Red Sox hosted, and swept, a twin-bill against Oakland on Aug. 27 (a mere 11 days after another double-header, this one against the Rays). The sweep gave them a two-game lead over the Yankees in the A.L. East, and the only question seemed to be whether they would hold that lead or settle for the Wild Card. They managed neither. They crashed to a 7-20 record over the next 30 days, a span that included two more double-headers on Sept. 19 and 25 (both splits). By the end of that stretch, they were far behind the Yankees, tied with Tampa Bay, and fighting for their playoff lives—a fight they would lose in Baltimore on the final day of the season, wasting a 90-72 record.

Were double-headers the secret culprits in the famed twin collapses of 2011? It’s tough to say that double-headers caused the slumps—for one thing, Atlanta was already sliding before playing two in Queens—but if they contributed even one loss, that’s decisive. I’ve already shown that the 30-day effect is closer to one game lost than zero, so it is at least an arguable point.

The Braves and Red Sox did have bad luck with double-headers that year. There were 34 played in 2011, coming out to 2.267 per team. (Remember, it’s two teams playing the games.) Atlanta ended up playing three that season, while the Braves’ eventual tormentor St. Louis played only one, and that way back in April. Boston had to play five twin-bills, as many as any team in baseball, while Tampa Bay played two fewer in the course of overhauling the Sox. The margin between the Sox and Rays over the last five weeks of the season was three to one, a bit of a drag chain on Boston’s stretch drive.

But double-headers are not destiny. The best record in baseball in 2011 belonged to the Philadelphia Phillies, who played four double-headers. Leading the American League standings were the New York Yankees, who played five, the same number as Boston—and they had three in the final five weeks of play, the same as Boston, during which New York gained nine games on their arch-rivals. The worst team in the majors, the Houston Astros, didn’t have to play a single twin-bill all season.

Teasing out a single cause for the falls of Boston and Atlanta and assigning all blame there is dubious at best. You could look at a hundred different hiccups and stumbles apiece for the teams, and say there, there was the decisive game lost. But it does concentrate the mind on the effect that double-header fatigue can have.

It also puts a new gloss on the near-extinction of the scheduled double-header, a cause of lamentation for baseball traditionalists. We may have lost a bit of baseball culture, not to mention a bargain for our entertainment dollars. Baseball, though, may have inadvertently gained a more even playing field. There is now virtually no pre-planned 18-inning extra strain on particular teams that could cost them a loss here or there—a loss that might change the trajectories of their whole seasons.

There are the unplanned double-headers, of course, but that ends up being the luck of the draw, or at least the residue of local climate and an open-air ballpark. One could, if so inclined, study how many postponements and thus double-headers a roofed stadium prevents each year, figure out how many wins that saves, assign dollar values to those wins, and calculate whether the extra cost of a roof on one’s ballpark is compensated by the extra revenue produced by the margin of additional wins that roof provides.

If you want to try that, I wish you luck. Personally, I’m going to delve into those old-time double-headers now. Sounds a lot less complicated.

References & Resources
Baseball-Reference and Retrosheet were as invaluable as usual.

A writer for The Hardball Times, Shane has been writing about baseball and science fiction since 1997. His stories have been translated into French, Russian and Japanese, and he was nominated for the 2002 Hugo Award.
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Scheduled doubleheaders have happened recently. The A’s and Angels had a scheduled doubleheader July 16, 2011. It was a long day, but this fan suffered no hangover effect

Shane Tourtellotte
Shane Tourtellotte

Kent:  Right you are.  Retrosheet has it listed there in the 2011 schedule—but the field that is supposed to identify double-headers incorrectly lists them as single games.  I’m about to send Retrosheet a little note to that effect.  Thanks for pointing this out.

Gary Hogan
Gary Hogan

Seriously?  An effect of one game over a month?  And this is blamed on playing a game in which nobody does anything strenuous except pitchers and catchers?  And I say that as a big baseball fan (Cardinals).  Just not buying this silliness. I think the author’s analytical skills could be employed to more useful effect elsewhere.